An interesting alternative to olefin production from petroleum is olefin synthesis from methanol. Methanol is considered to be a readily storable and manageable intermediate product for utilization of hitherto unused natural gas. Thus, the increasing demand for olefin could also be served through the use of very cheap methane. For this reason, processes are being developed that obtain short-chain olefins from methanol. Such processes operate, for example, catalytically according to the overall equation 2CH3OH→C2H4+2H2O. Besides the desired olefins, ethylene and propylene, undesired by-products also arise in the catalytic process. One undesired by-product is dimethyl ether. The problem of removing dimethyl ether from the product stream has not been satisfactorily solved up to now. Special absorber materials that are supposed to remove the dimethyl ether from the product stream have already been considered. However, it is difficult to find a suitable absorber or adsorber material for this purpose.